Pyrolytic Characteristics and Kinetics of Phragmites australis

Table 2

Algebraic expressions of functions 𝐺(𝛼) and 𝑓(𝛼) and mechanisms [23, 24].

No.	𝐺(𝑎)	𝑓(𝛼)	Rate-determining mechanism
1	1−(1−𝛼)^2/3	3/2(1−𝛼)^1/3	Chemical reaction
2	1−(1−𝛼)^1/4	4(1−𝛼)^3/4	Chemical reaction
3	(1−𝛼)^−1/2−1	2(1−𝛼)^3/2	Chemical reaction
4	(1−𝛼)^−1−1	(1−𝛼)^2	Chemical reaction
5	(1−𝛼)^2−1	1/2(1−𝛼)^3	Chemical reaction
6	(1−𝛼)^3−1	1/3(1−𝛼)^4	Chemical reaction
7	1−(1−𝛼)^2	1/2(1−𝛼)	Chemical reaction
8	1−(1−𝛼)^3	1/3(1−𝛼)^2	Chemical reaction
9	1−(1−𝛼)^4	1/4(1−𝛼)^3	Chemical reaction
10	𝛼^3/2	2/3𝛼^−1/2	Nucleation
11	𝛼^1/2	2𝛼^1/2	Nucleation
12	𝛼^1/3	3𝛼^2/3	Nucleation
13	𝛼^1/4	4𝛼^3/4	Nucleation
14	𝑙𝑛𝑎	𝛼	Nucleation
15	−𝑙𝑛(1−𝛼)	1−𝛼	Assumed random nucleation and its subsequent growth
16	[−𝑙𝑛(1−𝛼)]^2/3	3/2(1−𝛼)[−𝑙𝑛(1−𝛼)]^1/3	Assumed random nucleation and its subsequent growth
17	[−𝑙𝑛(1−𝛼)]^1/2	2(1−𝛼)[−𝑙𝑛(1−𝛼)]^1/2	Assumed random nucleation and its subsequent growth
18	[−𝑙𝑛(1−𝛼)]^1/3	3(1−𝛼)[−𝑙𝑛(1−𝛼)]^2/3	Assumed random nucleation and its subsequent growth
19	[−𝑙𝑛(1−𝛼)]^1/4	4(1−𝛼)[−𝑙𝑛(1−𝛼)]^3/4	Assumed random nucleation and its subsequent growth
20	[−𝑙𝑛(1−𝛼)]^2	1/2(1−𝛼)[−𝑙𝑛(1−𝛼)]^−1	Assumed random nucleation and its subsequent growth
21	[−𝑙𝑛(1−𝛼)]^3	1/3(1−𝛼)[−𝑙𝑛(1−𝛼)]^−2	Assumed random nucleation and its subsequent growth
22	[−𝑙𝑛(1−𝛼)]^4	1/4(1−𝛼)[−𝑙𝑛(1−𝛼)]^−3	Assumed random nucleation and its subsequent growth
23	𝑙𝑛𝑎/(1−𝛼)	𝑎/(1−𝑎)	Branching nuclei
24	𝛼	(1−𝑎)^0	Contracting disk
25	1−(1−𝛼)^1/2	2(1−𝑎)^1/2	Contracting cylinder (cylindrical symmetry)
26	1−(1−𝛼)^1/3	3(1−𝑎)^2/3	Contracting sphere (spherical symmetry)
27	𝛼^2	1/(2𝑎)	One-dimensional diffusion
28	[1−(1−𝛼)^1/2]^1/2	4{(1−𝛼)[1−(1−𝛼)]^1/2}^1/2	Two-dimensional diffusion
29	𝑎+(1−𝛼)𝑙𝑛(1−𝛼)	[−𝑙𝑛(1−𝛼)]^−1	Two-dimensional diffusion
30	[1−(1−𝛼)^1/3]^2	(3/2)(1−𝛼)^2/3[1−(1−𝛼)^1/3]^−1	Three-dimensional diffusion, spherical symmetry
31	1−2/3𝛼−(1−𝛼)^2/3	(3/2)[(1−𝛼𝑎)^−1/3−1]^−1	Three-dimensional diffusion, cylindrical symmetry
32	[(1−𝛼)^−1/3−1]^2	(3/2)(1−𝛼)^4/3[(1−𝛼)^−1/3−1]^−1	Three-dimensional diffusion
33	[(1+𝛼)^1/3−1]^2	(3/2)(1+𝛼)^2/3[(1+𝛼)^1/3−1]^−1	Three-dimensional diffusion
34	1+2/3𝛼−(1+𝛼)^2/3	(3/2)[(1+𝛼)^−1/3−1]^−1	Three-dimensional diffusion
35	[(1+𝛼)^−1/3−1]^2	(3/2)(1+𝛼)4/3[(1+𝛼)^−1/3−1]^−1	Three-dimensional diffusion
36	[1−(1−𝛼)^1/3]^1/2	6(1−𝛼)2/3[1−(1−𝛼)^1/3]^1/2	Three-dimensional diffusion